Practice Questions
Concept Explanation
When two ingredients form a mixture, their quantities are inversely related to how far each price is from the mean price. The ratio of ingredients can be found directly or via alligation.
Key Formulas
- Ratio Q1 : Q2 = (C2 − m) : (m − C1) where m is mean price
- Total parts = sum of ratio parts; each quantity = (its part / total parts) × total quantity
Example
Mean Rs. 24/kg from Rs. 20/kg and Rs. 32/kg. Ratio = (32 − 24) : (24 − 20) = 8 : 4 = 2 : 1.
Common Trap
Cheaper ingredient corresponds to (dearer − mean), not (mean − dearer).
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Q1 Easy
Mix at Rs. 24/kg from Rs. 20/kg and Rs. 32/kg. Ratio is:
ExplanationRatio = (32 − 24) : (24 − 20) = 8 : 4 = 2 : 1. -
Q2 Easy
Rs. 15/kg and Rs. 25/kg mixed to Rs. 20/kg. Ratio cheaper : dearer is:
Explanation(25 − 20) : (20 − 15) = 5 : 5 = 1 : 1. -
Q3 Medium
30 kg mixture in ratio 2 : 3 at Rs. 40 and Rs. 55/kg. Total cost is:
Explanation12 kg × 40 + 18 kg × 55 = 480 + 990 = Rs. 1410. -
Q4 Easy
Milk : water = 5 : 3 in 32 L. Milk is:
ExplanationMilk = 5/8 × 32 = 20 L. -
Q5 Medium
Rs. 10/kg and Rs. 16/kg to get Rs. 13/kg. Ratio cheaper : dearer is:
Explanation(16 − 13) : (13 − 10) = 3 : 3 = 1 : 1. -
Q6 Medium
40 kg in ratio 3 : 5 at Rs. 18 and Rs. 26/kg. Mean price is:
Explanation15×18 + 25×26 = 270 + 650 = 920. Mean = 920/40 = Rs. 23/kg. -
Q7 Easy
Tea Rs. 60/kg and Rs. 90/kg for Rs. 75/kg. Ratio dearer : cheaper is:
ExplanationCheaper : dearer = (90 − 75) : (75 − 60) = 15 : 15 = 1 : 1.
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Q8 Easy
48 L mixture, ratio 1 : 3. Smaller part is:
ExplanationSmaller part = 1/4 × 48 = 12 L. -
Q9 Medium
Rs. 8/kg and Rs. 14/kg for Rs. 11/kg. Ratio cheaper : dearer is:
Explanation(14 − 11) : (11 − 8) = 3 : 3 = 1 : 1. -
Q10 Hard
50 kg, ratio 4 : 1, at Rs. 30 and Rs. 50/kg. Total cost is:
Explanation40×30 + 10×50 = 1200 + 500 = Rs. 1700. -
Q11 Easy
Alcohol : water = 7 : 3 in 50 L. Alcohol is:
ExplanationAlcohol = 7/10 × 50 = 35 L. -
Q12 Medium
Rs. 12/kg and Rs. 18/kg for Rs. 15/kg. Cheaper quantity share is:
ExplanationRatio cheaper : dearer = 3 : 3 = 1 : 1. Cheaper share = 1/2. -
Q13 Easy
36 kg in ratio 5 : 4. Larger part is:
ExplanationLarger = 5/9 × 36 = 20 kg. -
Q14 Hard
Which ratio (cheaper : dearer) gives mean Rs. 28/kg from Rs. 22 and Rs. 40/kg?
ExplanationCheaper : dearer = (40 − 28) : (28 − 22) = 12 : 6 = 2 : 1.
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DS1 Easy
What is the ratio of the two ingredients?
Statement IMean price is Rs. 20/kg from Rs. 15/kg and Rs. 25/kg.
Statement IIQuantities are in equal amounts.
ExplanationStatement I alone: ratio = 5 : 5 = 1 : 1. -
DS2 Easy
How much milk is in the mixture?
Statement IMilk : water = 5 : 3.
Statement IITotal mixture is 32 litres.
ExplanationNeed both: milk = 5/8 × 32 = 20 L.
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DS3 Medium
Is the cheaper ingredient more than half the mixture?
Statement IRatio cheaper : dearer = 2 : 3.
Statement IITotal mixture is 50 kg.
ExplanationII alone gives total only. I alone: cheaper = 2/5 = 40%, not more than half. -
DS4 Medium
What is the total cost of the mixture?
Statement I30 kg in ratio 2 : 3 at Rs. 40 and Rs. 55/kg.
Statement IITotal mixture weighs 30 kg.
ExplanationStatement I alone: 12×40 + 18×55 = Rs. 1410.